Download Chapter 4 Congruent Triangles (page 116)

Algebra Review
Radical Expressions
page 280
Essential Question
Can you solve an equation with a
square root radical?
Simplifying Radicals
In the next chapters, work will be
done with radicals, specifically
square root radicals,
5 or _____.
2 3
such as _____
What is a RADICAL?
If n is a positive integer that is greater than 1 and
a is a real number then,
n
a
where n is called the index, a is called the radicand,
and the symbol √ is called the radical.
Square Root - definition from Wikipedia
In mathematics, a square root (√) of a number x is a number r such that
r2 = x, or in words, a number r whose square (the result of multiplying the
number by itself) is x. Every non-negative real number x has a unique nonnegative square root, called the principal square root and denoted with a
radical symbol as √x. For example, the principal square root of 9 is 3,
denoted √9 = 3, because 32 = 3 × 3 = 9. If otherwise unqualified, "the
square root" of a number refers to the principal square root: the square root
of 2 is approximately 1.4142.
Square roots often arise when solving quadratic equations, or equations of
the form ax2 + bx + c = 0, due to the variable x being squared.
Every positive number x has two square roots. One of them is √x, which is
positive, and the other −√x, which is negative. Together, these two roots are
denoted ±√x.
Square roots of integers that are not perfect squares are always irrational
numbers: numbers not expressible as a ratio of two integers. For example,
√2 cannot be written exactly as m/n, where n and m are integers.
Square Root - easy definition
A number that when multiplied by itself equals
a given number.
Root
A number that, when multiplied by itself some
number of times, equals a given number.
n
a
2
a
a
Perfect Squares
Know these!
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
A RADICAL is in
simplest form when …
#1
No perfect square factor,
other than one,
is ________
under the radical sign.
Use this property from algebra!
ab  a b
Example (a)
18  9  2
 9 2
3 2
Example (b)
98  49  2
 49 2
7 2
Example (1)
60  2 15
Example (2)
50  5 2
Example (3)
48  4 3
Example (4)
600  10 6
Example (5)
3 80  12 5
Example (6)
5 24  10 6
Example (7)
3  27
 81
9
Example (8)
20  2
 40
 2 10
Example (9)
8 23 6
 24 12
 48 3
Example (13)
x  12  13
2
2
2
x  144  169
2
x  25
2
x  25
x5
2
Example (14)

x  4 3
2

2
8
2
x  16g3  64
2
x  48  64
2
x  16
x4
2
A RADICAL is in
simplest form when …
#2
No fraction,
is ________
under the radical sign.
Use this property from algebra!
a
a

b
b
Example (a)
3
3

5
5
Example (b)
4
16
16


5
5
5
A RADICAL is in
simplest form when …
#3
No fraction,has a radical in
the _________________.
denominator
Use a method called …
Rationalizing the Denominator,
by using this pattern.
a a  a  a  a  ( a)  a
2
2
Example (a)
1
18 2 18 2


2
2 2

9
2
Multiplying by

1 does not
change it’s value.
Example (b)
1
3 2 3 3 6


5 3
5 3 3
6

Multiplying by
1 does not
5
change it’s value.

Example (a) - AGAIN!
3
3 5
1

5
5
5
15

5
Example (b) - AGAIN!
1
4
16
5
16



5
5
5
5
4 5

5
Example (10)
12
4 3
3
Example (11)
2
14

7
7
Example (12)
10
3

9
3 30
RADICALS must
always be expressed in
simplest form!
Why?
So you are able to recognize
the patterns.
Assignment
Algebra Review on page 280
1 to 29 odd numbers
Assignment
Written Exercises on page 288
1 to 15 odd numbers
Be prepared for a quiz on Simplifying Radicals!
Can you solve an equation with a
square root radical?